It's been a couple years back (1947), but Covington Buccs began their modern era football program with an 8 game schedule. Seven of those eight were shutouts with Covington going 2-5. The only game where both teams scored was with Brookville who won 15-6. Except for that lone touchdown, every game that season would have been a shutout.
1973-1974 Tipp City Bethel took part in two seasons of shutouts, every game ended in xx-0. Bethel was the goose egg in everyone of those games.